One of the ways Harper Lee establishes a feeling of mystery in Chapter 1 is by starting out the story with a conundrum. The narrator starts out by telling us that her brother, Jem, got his arm badly broken when he was almost thirteen. We are already curious as to why the story starts out this way and why Jem's broken arm is significant to this novel.
Harper Lee's narrator argues with her brother as to what caused this incident. We start to empathize with the narrator as we remember our own childhoods and our own youthful disagreements with our siblings. Authors establish mystery by introducing characters/protagonists we come to care about and identify with; they do this by creating a foundational history of their lives, presenting a problem/crisis/enigma the protagonist is wrestling with, establishing dramatic tension by stretching out the climax, and in the midst of all this tension, using clues/foreshadowing to further deepen the mystery of the situation. We are told that Jem believes it all started when Dill came to visit one summer and put to them the idea of 'making Boo Radley come out.' At this point, our curiosity is piqued: who is Boo Radley?
Through Calpurnia, Lee again arouses the reader's sympathy with the portrayal of a very strict mother figure to both Jem and Scout.
'Our battles were epic and one-sided. Calpurnia always won, mainly because Atticus always took her side. She had been with us ever since Jem was born, and I had felt her tyrannical presence as long as I could remember.'
We also find out that Scout and Jem lost their mother when Scout was only two. We are told Jem is the most affected of the two by this loss and how, sometimes, in the middle of a game, 'he would sigh at length, then go off and play by himself behind the car-house.' Scout tells us that 'when he was like that, I knew better than to bother him.' By this time, Harper Lee has the reader well within her powers; we feel for these two motherless children. Our sympathies inspire us to enter into whatever sorrows or trials they endure; we want them to be successful in their quest for the truth.
As a character, Dill embodies our own curiosity regarding this mysterious figure, Boo Radley. Lee draws out the mystery further by having Scout and Jem regale us with tall tales about Boo Radley, the way children sometimes do when they are afraid of something/someone and they don't have the emotional maturity to handle the ramifications of their fear. Jem and Scout tell us that every bad thing that happens in Maycomb can be attributed to Boo Radlley; indeed, we smile when we hear that 'Radley pecans would kill you.' Lee even has the neighborhood scold and gossip, Miss Stephanie Crawford, relate how Boo stabs his father in the leg with a pair of scissors and how in the aftermath, Mrs. Radley runs screaming out into the street that Boo is killing them all. Despite the recommendation, Boo is not sent to an asylum; instead he spends some time in the county jail and then goes home. We find out that no one ever sees or hears from Boo again after he goes home. We are left to wonder if he is mentally unstable or just plain homicidal. Here's how Jem comically puts it:
'Boo was about six-and-a-half feet tall,judging from his tracks; he dined on raw squirrels and any cats he could catch,that’s why his hands were bloodstained—if you ate an animal raw, you could never wash the blood off.'
At the end of the chapter, Dill dares Jem to run up and touch the Radley house in order to lure Boo Radley out. Boo does not come out but Lee ends the chapter appealing to our childhood fears about a bogeyman who just might come out and get us.
'...as we stared out the street, we thought we saw an inside shutter move. Flick. A tiny, invisible movement and the house was still.'